Several real-life decisions involve combining sensory information and reward outcomes. Yet, most previous research in human and animal literature has focused on either economic [1] or sensory decision making [2] in isolation. Here, we find that humans combine sensory information with reward outcomes optimally in a visual search task where they detect the presence or absence of a familiar target object in a cluttered scene, and receive reward feedback based on correct vs. incorrect response. We present three additional findings: 1) Rare targets are missed even when the target is salient (replicating results from [3]). 2) Contrary to previous studies [3,4], we find a rapid and optimal influence of reward on sensory decision making and detection rates - humans behave as reward-maximizing agents and decide whether the target is present or not based on whichever maximizes their expected reward. Hence, the poor detection performance for rare targets can be corrected by changing the reward scheme. 3) A quantitative model based on reward-maximization accurately predicts human detection behavior in different target frequency and reward conditions. We use this model to illustrate how reward schemes can be designed to obtain high detection rates for any target frequency. Potential applications of our findings include improving detection rates in life-critical searches for rare targets (e.g., bombs in airline passenger bags, cancers in medical images).